Operation Closure Math Example 3

Follow the full solution, then compare it with the other examples linked below.

Example 3

easy
Are integers closed under multiplication? Test with \((-3) \times 4\) and \((-2) \times (-5)\).

Solution

  1. 1
    \((-3) \times 4 = -12\). Is \(-12\) an integer? Yes.
  2. 2
    \((-2) \times (-5) = 10\). Is 10 an integer? Yes.
  3. 3
    Integers appear to be closed under multiplication.

Answer

Yes — both products are integers
The product of any two integers is always an integer. Integers are closed under multiplication.

About Operation Closure

A set is closed under an operation if performing that operation on members of the set always produces a result that is also in the set. For example, integers are closed under addition.

Learn more about Operation Closure →

More Operation Closure Examples

Example 1 easy

Are whole numbers closed under addition? Test with (5 + 7) and (12 + 0). Explain what closure means.

Example 2 medium

Are whole numbers closed under subtraction? Provide a counterexample if not.

Example 4 medium

Are integers closed under division? Provide a counterexample if not.

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